Condition $\mathcal {B}$ and Baire $1$ generalized derivatives
HTML articles powered by AMS MathViewer
- by Udayan B. Darji, Michael J. Evans and Richard J. O’Malley PDF
- Proc. Amer. Math. Soc. 123 (1995), 1727-1736 Request permission
Abstract:
Ordered pairs (F, f) of real-valued functions on [0,1] which satisfy the condition that every perfect set M contains a dense ${G_\delta }$ set K such that $F\backslash M$ is differentiable to f on K are shown to play a key role in several types of generalized differentiation. In particular, this condition is utilized to prove the equivalence of selective differentiation and various forms of path differentiation under the assumption that the derivatives involved are of Baire class 1, thereby providing an affirmative answer, for Baire 1 selective derivatives, to a question raised in [Trans. Amer. Math. Soc 283 (1984), 97-125].References
- A. M. Bruckner, R. J. O’Malley, and B. S. Thomson, Path derivatives: a unified view of certain generalized derivatives, Trans. Amer. Math. Soc. 283 (1984), no. 1, 97–125. MR 735410, DOI 10.1090/S0002-9947-1984-0735410-1
- M. Laczkovich, On the Baire class of selective derivatives, Acta Math. Acad. Sci. Hungar. 29 (1977), no. 1-2, 99–105. MR 437691, DOI 10.1007/BF01896471
- R. J. O’Malley, Selective derivates, Acta Math. Acad. Sci. Hungar. 29 (1977), no. 1-2, 77–97. MR 437690, DOI 10.1007/BF01896470
- Udayan B. Darji and Michael J. Evans, Recovering Baire $1$ functions, Mathematika 42 (1995), no. 1, 43–48. MR 1346670, DOI 10.1112/S0025579300011335
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1727-1736
- MSC: Primary 26A24
- DOI: https://doi.org/10.1090/S0002-9939-1995-1254835-4
- MathSciNet review: 1254835